Calculator Inputs
Example Data Table
This sample illustrates how relative dispersion metrics compare the spread against the dataset center.
| Observation | Value | Deviation from Mean | Absolute Deviation |
|---|---|---|---|
| 1 | 12 | -3.625 | 3.625 |
| 2 | 15 | -0.625 | 0.625 |
| 3 | 17 | 1.375 | 1.375 |
| 4 | 13 | -2.625 | 2.625 |
| 5 | 18 | 2.375 | 2.375 |
| 6 | 20 | 4.375 | 4.375 |
| 7 | 16 | 0.375 | 0.375 |
| 8 | 14 | -1.625 | 1.625 |
Formula Used
Mean: μ = Σx / n
Standard Deviation: σ = √[Σ(x − μ)² / n] for population, or s = √[Σ(x − x̄)² / (n − 1)] for sample.
Coefficient of Variation: CV = (Standard Deviation / |Mean|) × 100
Relative Range: RR = (Maximum − Minimum) / |Mean| × 100
Relative Mean Absolute Deviation: RMAD = (MAD / |Mean|) × 100
Mean Absolute Deviation: MAD = Σ|x − μ| / n
Quartile Coefficient of Dispersion: QCD = (Q3 − Q1) / (Q3 + Q1) × 100
Relative dispersion converts absolute spread into percentages or ratios, making comparisons easier across datasets with different units or scales.
How to Use This Calculator
- Choose raw dataset mode for direct observations, or summary mode for known statistics.
- Select sample or population deviation based on your data context.
- Pick the main metric you want highlighted in the result panel.
- Enter values, summary fields, and preferred decimal precision.
- Click the calculate button to display results under the header and above the form.
- Use the CSV button for spreadsheets and the PDF button for shareable reports.
- Review the interpretation text to understand whether dispersion is low, moderate, or high.
FAQs
1. What does relative dispersion measure?
It measures spread after scaling by a central value, usually the mean or quartiles. This makes variability easier to compare across datasets with different sizes or units.
2. When should I use coefficient of variation?
Use it when you need a mean-based percentage spread and the mean is not zero. It is common in quality control, finance, science, and performance comparison.
3. Why can the result become undefined?
Mean-based relative metrics divide by the mean. If the mean is zero or nearly zero, the ratio becomes unstable or undefined. Quartile-based measures are safer there.
4. What is the difference between sample and population deviation?
Population deviation uses all members of the full group. Sample deviation adjusts the divisor to estimate spread from a subset, reducing bias in the estimate.
5. Why include quartile coefficient of dispersion?
It relies on quartiles rather than the mean, so it is more resistant to outliers and useful for skewed data or distributions with extreme values.
6. Can I compare datasets with different units?
Yes. Relative dispersion standardizes spread into ratios or percentages, so comparison becomes more meaningful even when raw scales differ substantially.
7. What is a good coefficient of variation?
There is no universal threshold. Lower values indicate tighter consistency, but acceptable dispersion depends on the field, measurement process, and business or research tolerance.
8. Can I export the result for reporting?
Yes. The calculator includes CSV export for spreadsheet workflows and PDF export for printing, sharing, or attaching results to reports and documentation.